Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
108 |
36 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
102 |
36 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
72 |
36 |
108 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
69 |
33 |
102 |
Molecule Parameter
Number of Atoms (N) |
36 |
Number of internal coordinates |
102 |
Number of independant internal coordinates |
69 |
Number of vibrational modes |
102 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
69 |
33 |
102 / 0 |
Quadratic (Raman) |
69 |
33 |
102 / 0 |
IR + Raman |
69 |
33 |
102 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
102 |
36 |
quadratic |
2 |
5.253 |
699 |
cubic |
3 |
182.104 |
9.624 |
quartic |
4 |
4.780.230 |
104.790 |
quintic |
5 |
101.340.876 |
956.592 |
sextic |
6 |
1.807.245.622 |
7.590.842 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
69 |
33 |
quadratic |
2 |
2.976 |
2.277 |
cubic |
3 |
95.864 |
86.240 |
quartic |
4 |
2.442.510 |
2.337.720 |
quintic |
5 |
51.148.734 |
50.192.142 |
sextic |
6 |
907.418.232 |
899.827.390 |
Literature
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
- X.F. Zhou, P. Pulay. J. Comp. Chem. 10 No. 7, 935-938 (1989)
Characters for Symmetric and Antisymmetric Higher Powers of Representations:
Application to the Number of Anharmonic Force Constants in Symmetrical Molecules
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement